JEJU, South Korea — The annual Jeju Forum for Peace and Prosperity is an occasion for meeting and greeting friends and contacts, listening to experts on a wide range of topics and savoring sumptuous dining at the International Convention Center overlooking the rocky coast of this verdant Korean island province.

After all the friendly exchanges are done, however, one impression emerges: the North Korean nuclear issue is further than ever from resolution, and nobody knows what to do about it. Nor is it clear where South Korea is going in its alliance with the United States despite sharing the values and forms of democracy and capitalism embellished by freedom of speech and freedom to worship (or not worship).

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Participants in the forum refrained from insults and name-calling, but their differences were obvious as they reflected the viewpoints of countries locked in an unending standoff for power and influence from the western Pacific to the South China Sea. Americans and Koreans were just as likely to agree as to disagree, raising the question of how long the special relationship can endure despite the claims of U.S. Defense Secretary Jim Mattis and Secretary of State Rex Tillerson that the United States and South Korea are “in lockstep.”

The failure of anyone to come up with a solution to the North Korean conundrum means to some observers that maybe the problem is insoluble. Gary Samore of the Belfer Center at Harvard, formerly with the Obama administration, evinced that sentiment in a wide-ranging discussion on “the future of geopolitics in East Asia.” That sense weighs heavily on policymakers in Seoul as well as Washington.

How can the Koreans and Americans agree on a common approach when they have no realistic idea what to do?

Indecision has never been higher than now as South Korea’s new president, Moon Jae-in, fantasizes dialogue and reconciliation and President Donald Trump seems unable to decide where he stands. Would he really like sitting down with Kim Jong-un for a hamburger or would he prefer a “pre-emptive strike” against the North’s nuclear and missile facilities?

Judging from all that was said here, the American and South Korean presidents may never come to an understanding on North Korea.

Moon would doubtless like to persuade North Korea’s Kim Jong-un to stop the testing long enough to be able to follow through on gestures toward reconciliation. Trump, meanwhile, is waiting to see if China’s President Xi Jinping can restrain the North. If Xi fails, Trump may take matters into his own hands with results that are difficult to anticipate. No one, possibly including Trump, knows what Trump will do.

One thing is sure: Moon and Trump will not see eye to eye if Trump gives up on the Chinese and chooses a military option. North Korean missile tests so far have aroused only denunciations and tighter sanctions, but the threat of a long-range intercontinental ballistic missile capable of carrying a nuclear warhead to the United States might induce Trump to act precipitously.

Might Trump want to strike if China does not respond by cutting off the North’s oil supply?

These questions are sure to test not only the historic South Korea-U.S. alliance but an array of values that bind the two countries together in ways that may define precise definition. South Korean democracy may be far from perfect, but it comes much closer to the democratic ideal than almost any other nation for which Americans have fought and died since World War II.

It’s possible for Koreans to forget the bonds they have formed with the United States, but they exist on all levels from military to academic, from commerce to entertainment, from scientific to artistic. Differences over North Korea are sure to test that relationship when Moon sees Trump in Washington.

The history of the alliance, however, will compel the presidents of South Korea and the United States to listen carefully to each other in an effort at coordinating closely on North Korea as on other issues. The rise of democracy in South Korea adds to the urgency for these two leaders, however they disagree, to sublimate their more extreme views in the interests of preserving the alliance.

The security of South Korea, the balance of power in Northeast Asia and the Pacific, and the rights and interests of Koreans as well as Americans are at stake as they build on today’s relationship in hopes of a better tomorrow.

Donald Kirk has been a columnist for Korea Times, South China Morning Post many other newspaper and magazines. He wrote this for InsideSources.com.